Solve for $x$ : $3x^2 + 6x - 105 = 0$
Explanation: Dividing both sides by $3$ gives: $ x^2 + {2}x {-35} = 0 $ The coefficient on the $x$ term is $2$ and the constant term is $-35$ , so we need to find two numbers that add up to $2$ and multiply to $-35$ The two numbers $-5$ and $7$ satisfy both conditions: $ {-5} + {7} = {2} $ $ {-5} \times {7} = {-35} $ $(x {-5}) (x + {7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -5) (x + 7) = 0$ $x - 5 = 0$ or $x + 7 = 0$ Thus, $x = 5$ and $x = -7$ are the solutions.